Forward volatility implied by SPX options, and that of VIX futures get out of line. If there existed VIX SQUARED futures they could easily be replicated (and arbitraged) with a strip of SPX options. However replicating VIX futures would theoretically require dynamic trading in options (all strikes) and is also would depend on the model for distribution of vol of vol.

Question for traders: have you or someone you know ever traded SPX options (variance) vs VIX futures, and if yes then please provide some clues. Please don't write that there is an academic article about this; I'm asking if someone did this is practice.

2 Answers
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Short answer: yes.
Long answer: the challenge in trading these things, like you mentioned, is that each contract is not perfectly hedgable. This is an intentional choice made by the exchanges that list these products, so that they can provide an incentive to trading firms(locals) to provide liquidity for these new products and help boost trading volume.

The primary challenge in trading spx options vs vix futures, or spx options vs vix options, or vix options vs vix futures, is the fact that all three have different expirations.
This fact combined with the wildly different notionals for each (vix futures = 1000*vix, vix options = 100 * vix, and spx = 250*vix) makes it more difficult to hedge and trade one versus the other.

What most liquidity providers do instead of trying some kind of variance-gamma model approach is to simply hedge vix options or vix futures using spx straddles, and updating their hedges several times a day. This isn't a perfect hedge, and has lots of additional timing risks. However, there is something like 1% to 1.5% edge in trading this approach, so levering up can make it a reasonable strategy when considered with mean reverting nature of vix.